Inflation, income distribution nexus. A pathway to Nigeria's long term socioeconomic development. A chain rule effect

doi:10.21203/rs.3.rs-5238821/v1

This study is aimed at analyzing income distribution as a pass through for the effect of inflation on socio-economic development in Nigeria. Annual time series data from 1981 to 2023 was utilized. The Autoregressive Distributed Lag (ARDL) Bounds testing procedures was used including pre and post-test to ensure the accuracy of this method. Additionally, the chain rule was equally used to determine the transmission mechanism (channel) and the interactive level of income distribution on socio-economic development. The results indicates the presence of a long-run relationship among inflation, income distribution, and socio-economic development, as confirmed by ARDL Bounds test. The result shows that inflation has a negative but significant impact on socio-economic development in Nigeria with income distribution serving as a transmission channel (mechanism). Based on these findings, it is suggested that the government should implement various strategies and policies, including redistribution policies, plans that will promote socio-economic development.

JEL classification: E31, D30, O11, C1

h Nigeria, a country with vast natural resources and a large population, has struggled to achieve sustainable socio-economic development. Two key challenges facing the country which it has struggled with are inflation and income inequality, which have hindered socio-economic development. Inflation, income distribution, and socio-economic development are interconnected issues that require a comprehensive approach to address. They have remained significant challenges to Nigeria's socioeconomic development, with the country experiencing persistent double-digit inflation rates and a widening income gap between the rich and the poor which continues to be a source of concern to both the public and the government. For instance, in 1984, when the Naira was devalued and an increase in money supply, inflation rate increased to 41.2 per cent with income inequality, as measured by the Gini Index was 30.4. The clamor for an increase in minimum wage instead of equity in income distribution by the Nigerian Labor Congress (NLC) caused inflation to rise again between 1988 and 1989 to 56.04 and 50.47 per cent respectively which rather further widened the income gap to 47.25.

Between 1991-94 Nigeria was pressurized to devalue the currency. With the belief that devaluation was forthcoming further increase inflation to averaged 40 per cent as price adjusted to the parallel exchange rate (Okere and Sanni, 2005) with income distribution averaged 55.2. In 2016 and 2021, inflation rate averaged 13.74 per cent and 28.92 per cent in December 2023 (NBS, 2023) leaving income distribution to an average of 42.12 and 47. 2 in 2023. Evidently, given the data of income distribution against inflation rate, it can be deduced that a wide income distribution gap paves the way for an increase in inflation. Though it is established that when income distribution is perfect, it is most likely not good for the economy. The reason is that the poor tend to have a high marginal propensity to consume while the rich tend to invest the more rather than consuming. This on its own continues to widened the income gap in Nigeria.

Though controlling or checkmating income variation is not a mandate of the Central Bank of Nigeria. However, this menace caused the monetary authority in partnership with the fiscal authority to be involved in providing various intervention through the initiation of various policies, schemes and programmes that would help reduce variation in income distribution with the intent of tackling inflation. This is so because it is believed that an increase in income inequality directly affects prices which also contributes to increase in inflation vice-versa, which the Central Bank strives to reduce (Li and Zou, 2002 and Monninn 2014). Examples of such policies initiated include the money transfer, market money, loans to farmers, grants and loans to small and medium enterprise through NIRSAL, survival fund, N-power, conditional cash transfer (CCT), government enterprise and empowerment program (GEEP), etc. which comes under the National Social Investment Program of Nigeria created by the Federal government of Nigeria in 2015 to ensure a more equitable distribution of resources to vulnerable populations including children, youth and women. In the cause of implementing these policies and programmes, it is believed and assumed that the gap in income inequality would be closed while beneficiary would invest such funds in productive activities which would in turn increase supply of goods so as to reduce inflation and bring about socio-economic development in Nigeria.

Despite efforts to address these issues, the country's socioeconomic development remains sluggish, with many citizens struggling to meet their basic needs. The relationship between inflation, income distribution, and socioeconomic development in Nigeria is not well understood, and there is a need to investigate how these variables interact and impact the country's development. This study aims to provide a better understanding of these relationships and identify policies that can reduce inflation and bring about a better redistribution of income which would lead to a long term socio-economic development in Nigeria.

The thrust of this study is therefore to unravel the specific effects and empirically assess the relationship between inflation, income distribution as a pathway for Nigeria’s long term socio-economic development and understand how income distribution can serve as a transmission mechanism through which the socio-economic development can be affected by inflation. Unearthing this transmission effect will show the extent to which reduction in inflation and income distribution can help at achieving socio-economic development in Nigeria. An understanding of the mechanism is prerequisite for the successful conduct and adoption of economic policies to tackle the menace of inflation through the income distribution channel in Nigeria. Following this section is section 2 which covers the conceptual literature, literature review, theoretical framework and the gap the study intends to fill, while in section 3 the study’s methodology is presented. Section 4 covers the result analysis while section 5 takes a look at the conclusion and policy recommendations.

2.1 Conceptual literature

a. Inflation: Inflation can be defined as the rate at which the general level of prices for goods and services is rising. Inflation means a sustained increase in the aggregate or general price level in an economy. Inflation has also been defined by scholars from countries based on antecedence occurrence on their economies. It is also defined as a situation of rapid, persistent and unacceptable high rise in the general price level in an economy resulting to general loss of purchasing power (Afolabi & Olayemi, 1995)

b. Income distribution: This is said to be discrepancies that exist in the income between the three income group (the poor, middle class, and the rich), those on the same level in terms of academic qualification etc. As a measure of income distribution, the Gini coefficient (index) would be used as it captures the index of the three income group that exist.

c. Socio-economic development: This means the improvement of people’s lifestyles by way of improving their education, incomes, skills development and creating employment for the unemployed. Furthermore, it is the process of economic and social change based on cultural and environmental and cultural features.

2.2 Theoretical framework

The theoretical basis of the study is human capital theory and the chain rule. The human capital theory focuses on education and human skills as key drivers of development as propounded by Schultz (1963). The chain rule was first being used by Gottfried Wilhelm Leibniz in 1676 (with a sign error in calculation). He used it to calculate the derivative of $\:\sqrt{a+bz+\:{cz}^{2}}$ as the composite of the square root function and the function $\:a+bz+\:{cz}^{2}.\:$ The common notation of the chain rule is thus due to Leibniz. It is believed that the first modern version of the chain rule appears in Lagrange’s 1797 “theorie des functions analytiques”. It also appears in Cauchy’s 1823 “Resume des Lecons donnees a L’Ecole Royale Polytechnique Sur Le Calcul infinistesinal”.

In calculus, the chain rule is a formular that expresses the derivative of the composition of two differentiable functions f and g in terms of the derivative of f and g. More precisely, if h = f o g is the function such that h(x) = f(g(x)) for every x, then the chain rule is in Lagrange’s notation;

h’(x) = f’ (g(x)) g’(x) (1)

or equivalently

h’ = (f o g )’ = (f’ o g) * g’ in Leibniz’s notation. (2)

If a variable z depends on the variable y which itself depends on the variable x (that is y and z are dependent variables), then z depends on x as well, via the intermediate variable y. In this case, the chain rule is expressed as

$\:\frac{dz}{dx}$ = $\:\frac{dz}{dy}$ * $\:\frac{dy}{dx}$, (3)

$\:\frac{dz}{dx}$ $\:\begin{array}{c}\\\:x\end{array}$ = $\:\frac{dz}{dy}$ $\:\begin{array}{c}\\\:y\left(x\right)\end{array}$ * $\:\frac{dy}{dx}$ $\:\begin{array}{c}\\\:x{\prime\:}\end{array}$ (4)

For indicating at which points the derivatives have to be evaluated. The chain rule is important because many useful functions are compositions of other functions. That rule tells how to find the derivative of the composite.

For this study, the chain rule is applied so as to get the coefficient and the magnitude of the transmission mechanism from income distribution inflation as its affects socio-economic development. This is so because in the course of this study, inflation (z) depends on income distribution (y), which depends on socio-economic development (x) that is, y and z are dependent variable, then z depends on x as well, via the intermediate variable y.

2.3 Empirical literature

The relationship between inflation, income distribution and socio-economic development is dearth.. Though several studies has been done on the relationship between inflation and growth, inflation and income distribution, income distribution and growth. The study by Ali and Asfaw, (2023) aims to analyze the relationship between inflation, income inequality, and economic growth in Ethiopia using advanced statistical techniques such as VEC (vector error correction) model with Granger causality, and Johansen’s cointegrated. The study covers the period from 1980 to 2022 and includes pre and post-estimation diagnosis tests to ensure the accuracy of the model. The results indicate the presence of a long-run relationship among inflation, income inequality, and economic growth, as confirmed by Johansen’s cointegrated test. Based on the findings, the authors suggested that government should implement various strategies and policies, including redistribution policies, social safety nets, promoting inclusive economic growth, coordinating effective monetary and fiscal policies, implementing progressive taxation, and reforming the labor market.

Okoh and Ibrahim (2021) examined the impact of income inequality on economic development in Nigeria between 1989 to 2020. The objectives of the study were to examine if Gini coefficient has a significant impact on per capita income in Nigeria, to ascertain if poverty rate has a significant impact on per capita income in Nigeria and to determine if inflation rate has a significant impact on per capita income in Nigeria. The study used multiple linear regression to analyze the data. The result of the study shows that income inequality as proxied by Gini coefficient and poverty rate has a negative and significant impact on per capita income, while inflation rate has a negative but insignificant impact on per capita income in Nigeria. The study recommended that government should direct its policies and programs towards measures that enhance income redistribution, as it would reduce the level of inequality and ensure an even distribution of income.

The study by Özdemir (2020) examined the relationship between inflation and income distribution (measured with labor share of income). In estimation, the author used fixed effect balanced panel dataset within the period of 1980 to 2017 for selected 19 advanced economies. The results shows that an increase in inflation will unexpectedly increase the income shares accrued to labor and a higher degree of unionization will increase the labor’s share. The positive effect of inflation was lessened by higher degree of unionization and unemployment rate. The study therefore recommends that, the economic authorities should consider fallback options of workers as they may have either direct or indirect effects on income distribution through its interaction with inflation.

The result of the study carried out by Muhibbullah and Mala Rani Das (2019) in their study of inflation on income inequality using data from the period of 1990 to 2015 shows that inflation has a positive significance effect on income inequality. Using time series data and the vector error correction model (VECM), the Johannsen co-integration test confirm that there is a long-run positive significant relationship among the examined variables.

In another study by Monnin (2014), the author investigated the empirical link between income inequality and inflation in ten OECD countries over the period 1971 to 2010. The study estimated the empirical link between all seven variables and income inequality with a balanced panel. The result shows a U-shaped link between long-run inflation and income inequality.

Inflation among other variables was seen as one of the main determinants of income distribution as carried out in the study by Skare and Stjepanovic (2014) showing the relationship between income distribution and other relevant economic variables. Panel data analysis was used to study 200 world economies and identify main income determinants. The results of the paper shows that there was a large inconsistency of income distribution measured by household consumption for different classes.

Using the econometric regression model analysis on a monetarists’ approach and the Vector Auto regression, Galli and von der Hoeven (2011) claim that there is a long run relationship between inflation and income inequality. Their empirical analysis is implemented for the USA using a sample of 15 OECD countries using annual data for the period 1997–2007.

Heer and Sussmuth (2003) showed the effect of a permanent change of inflation on the distribution of wealth. The study was analyzed in a general equilibrium OLG model that is regulated with regard to the characteristics of the US economy. The study showed that an increase in inflation results in a lower stock market participation rate; in addition, the distribution of wealth becomes more unequal, even though the quantitative effect is economically negligible.

The paper by Hongyi and Zou (2002) title Inflation, growth, and income distribution used a Cross-Country for a time period from 1950 to 1992. The study used a newly compiled cross-country panel data on income distribution to explore the impact of inflation on income distribution and economic growth. Averaged data spanning over 5-year periods was utilized in their empirical analysis. The results showed that inflation worsens income distribution; increases the income share of the rich; has a negative but insignificant effect on the income shares of the poor and the middle class; and reduces the rate of economic growth.

Li and Zou (2002) in their study using cross-country panel data for South Korea covering the period 1990–2000, using the Ordinary Least square method investigated the impact of inflation on income distribution. The result of the study shows that inflation deteriorates income distribution and economic growth. They also show that inflation increases the income share of the rich and insignificantly reduces the income shares of the middle class and the poor.

The study title Income Inequality: Does Inflation Matter?, by Bulir (2010) using cross-country data, and applying the Vector Auto-Regression approach for Germany provides evidence that previous inflation raises income inequality between the periods of 1959 to 2006. The study found no significant relationship between inflation and income inequality. The result shows that the positive effect of price stability on income inequality is nonlinear. The author concludes that price equilibrium is useful for reducing income inequality not only through its direct outcome but also indirectly through boosting money demand and preserving the real value of fiscal transfers.

The study by Albanesi (2007) provides cross-country evidence of positive correlation between inflation and income inequality. The result shows that for the government it is easier to finance its spending through positive seignior-age than via increased taxation, which requires parliamentary approval. This leads to inflation in equilibrium and to its positive relation with income inequality. Therefore, low income households are more exposed to inflation.

2.3.2 Research gap

This study is a departure from other existing literature reviewed or a point of departure from the studies reviewed particularly those connected to Nigeria is that to the best of my knowledge none of them truly simultaneously examined the role, interactive impact and magnitude of the transmission of income distribution as a mechanism through which inflation affects socio-economic development as done in this study. Rather a direct independent effect from inflation to income distribution and socio-economic development as can be seen in the literature. This study also provides by calculating and filling in the gaps of Gini coefficient for the period this study covers.

This study employed a quasi-experimental research design. This design is used to establish the fundamental relationship between the dependent variable and the independent variables in such a way that the researcher cannot manipulate the outcome of the results since the events are antecedent to the investigation.

Model specification

HDI _t = $\:\beta\:$₀ + $\:\beta\:$₁INF_t + $\:\beta\:$₂ln(RGDP) + $\:\beta\:$₃PCI_t + β₄POV_t + β₅UNEM_t−1$\:\:+{\beta\:}$₆IND_t + ε_t (5)

Interactive impacts

To institute the interactive impacts of income distribution on socio-economic development, a general to specific interactive specification was adopted (Okoh and Ebi; 2013, Abang, 2023). The general equation is as depicted in Eq. 1. From the general equation, we specified the specific equation by removing the variable of income distribution from Eq. 5. The reason for the interactive impact is to find out the behaviour of the determinant and coefficient of socio-economic development (HDI). Thus the specific equation without income distribution variable is as below:

HDI _t = α₀ + α₁INF_t + α₂ln(RGDP) + α₃PCI_t + α₄POV_t + α₅UNEM_t−1$\:\:$ + ε_t (6)

Furthermore, for the reason that income distribution is a function of socio-economic development, income distribution is also treated as an endogenous variable as captured in Eq. 3.16 below:

IND _t = λ₀ + λ₁INF_t + λ₂ln(RGDP) + λ₃PCI_t + λ₄POV_t + λ₅UNEM_t$\:\:+$ λ₆HDI_t + ε_t (7)

The transmission mechanism (channel) income distribution as a pass through for monetary policy effect on inflation

The primary question of this study relates to the transmission channel (effect) of income distribution to inflation as it affect socio-economic development. To this end we examine the indirect effect of income distribution by which inflation passes through to affect socio-economic development. Thus the chain rule effect was be applied to derive the actual coefficients for the transmission mechanism (Ebi & Aladejare; 2022, Abang, 2023). This thus implies that the magnitude and the pass through effect of income distribution on socio-economic development through inflation is anchored on the chain rule. The chain rule is used to show how to evaluate a derivative when variable’s effect works through one function embedded in another. Thus the simplest form of the chain rule is for real value functions of one real variable. It states that if g is a function that is differentiable at g(c), then the composite function f o g is differentiable at C, and the derivative is

(f o g)’ (c ) = f’(g(c )) * g’(c )

If y = f(u) and u = g(x), then this abbreviated form is written in Leibniz notation as:

$$\:\frac{\partial\:y}{\partial\:x}\:\:=\:\frac{\partial\:y}{\partial\:u}\:\text{*}\:\frac{\partial\:u}{\partial\:x}$$

Carrying the same reasoning and applying it, the transmission channel of inflation passing through income distribution to have effect on socio-economic development:

If HDI = f (IND)

Then; IND = f (INF), HDI = f (INF)

Simply put:

$\:\frac{\partial\:HDI}{\partial\:IND}$ = $\:\frac{\partial\:HDI}{\partial\:INF}$ * $\:\frac{\:\partial\:INF}{\partial\:IND}$ = $\:\beta\:$₁ * λ₁ (8)

The coefficient of their product as in 8 above shows the coefficient and magnitude of transmission.

4.1 Descriptive statistics

As indicated in the Table 1 the mean values of inflation, income distribution, real gross domestic product, unemployment, per capita income, poverty and human development index were 18 per cent, 44.56, 37,365.08 billion, 4.60 per cent, 153,739.7, 30.06 per cent and 0.409 respectively

The maximum values of the respective variables were: 72.8 per cent, 73.9, 12,948.54 billion, 20,867.30 billion, 23.2 per cent, 65,098,319 million, 34,001.89 billion, 395 per cent, 2.16E + 08, 73,126.08 billion, 1,227.57 billion and 9.79 million. While the minimum values of the respective variables were: 4.67 per cent, 0.43, 9.64 billion, 11.2 billion, 5.7 per cent, 22,050,370 million, 16.16 billion, 0.61 per cent, 75,440,505, 13,779.26 billion, 0.22 billion and 3.6 per cent.

Skewness is a measure of the probability distribution of a real-valued random variable about it mean. A normal distribution is symmetrical at point 0. If the value is greater than zero it is positively skewed but if it is less than zero, it is negatively skewed. From result in Table 4 above, it is observed that all the variables have positive skewness except income distribution (IND) with a negative skewness of -0.44. Kurtosis measures the peakness or flatness of the distribution of the series. If the kurtosis is above 3, the distribution is peaked or leptokurtic relative to the normal and if the kurtosis is less than three, the distribution is flat or platykurtic relative to normal. From table above, all the variables are positive and greater than three, except real gross domestic product (RGDP) and human development index (HDI) which is the distribution is peak or leptokurtic. Thus, real gross domestic product (RGDP) and human development index (HDI) are flat or platykurtic relative to normal.

Table 1

Descriptive analysis on the selected variables captured in this study.
	INF	IND	RGDP	UNEM	PCI	POV	HDI
Mean	18.09833	44.56195	37365.08	4.604048	153739.7	30.02627	0.408824
Median	12.00000	42.56100	27112.63	3.790000	28719.62	25.67000	0.400000
Maximum	72.81000	73.91000	73126.35	9.790000	748290.6	84.71000	0.530000
Minimum	4.670000	0.430000	13779.26	3.590000	160.0800	7.600000	0.300000
Std. Dev.	15.99483	13.95011	21791.99	1.897583	224862.3	16.08805	0.059250
Skewness	1.951720	-0.434978	0.501227	1.889748	1.346192	1.506978	0.273420
Kurtosis	5.903862	4.135236	1.607140	4.811599	3.449407	4.899026	2.494355
Jarque-Bera	41.42121	3.579773	5.153704	30.74133	15.83315	26.96673	1.178762
Probability	0.000000	0.166979	0.076013	0.000000	0.000365	0.000001	0.554670
Sum	760.1300	1871.602	1569334.	193.3700	7840725.	1531.340	20.85000
Sum Sq. Dev.	10489.22	7978.831	1.956510	147.6336	2.536312	12941.28	0.175529
Observations	43	43	43	43	43	43	43
Source: Authors’ computation (2024)

4.2 Unit root test result

Table 2 shows the unit root test result. The unit root test was conducted with the aim of establishing the stationarity conditions of the variables. The test was based on the Augmented Dickey-fuller (ADF) test as well as the Phillips-Perron test. The result/ outcome of the tests as reported in Tables 2 revealed that variables such inflation rate, income distribution and poverty (POV) were all stationary at level. This is because their ADF and PP test statistics values calculated in absolute terms were greater than their respective tabulated values at the five per cent level of significance. The remaining variables such as per capita income (PCI), unemployment rate (UNEM), real gross domestic product (RGDP) and human development index (HDI) were however stationary after the performance of first difference operation on them. This means that the variables were integrated of mixed integrating orders I(0) and I(1). Given this scenario, the ARDL bounds testing approach was applied in testing for the cointegration among the variables.

Table 2

Stationarity test (Unit root test result)
Variable
	Level	1st Difference	Order of integration	Level 1st Difference Order of integration
PCI	-1.364750	-6.213502	I(1)	-1.352460 -6.217924 I(1)
POV	-3.753603	-	I(0)	-3.595522 - I(0)
UNEM	-0.437825	-5.991146	I(1)	-0.710466 -5.989214 I(1)
RGDP	0.000230	-2.608976	I(1)	0.850837 -2.609574 I(1)
HDI	-1.928149	-12.54360	I(1)	-2.664092 -7.233252 I(1)
INF	-4.489853	-	I(0)	-3.312418 - I(0)
IND	-3.944116	-	I(0)	-3.843640 - I(0)

ADF test critical test values. Phillip-Peron test critical values

Level: 1st Difference: Level: 1st Difference:

At 5% = -2.935001 5% = -2.938987 At 5% = -2.935001 5% = -2.926622

10% = -2.605836 10% = -2.607932 10% = -2.605836 10% = -2.601424

Source: Authors’ computation using Eviews 10 (2024)

4.3 Co-integration test

The result of the bounds test (co-integration test) as indicated in Table 3 showed that the computed F-statistic of about 8.95 was greater than the upper bound critical values of 3.99, 3.28 and 2.94 at the one per cent, five per cent and 10 per cent levels of significance. Since the computed F-statistic value has exceeded the upper critical bound values at the one per cent, five per cent and 10 per cent levels of significance, the null hypothesis of no co-integration is rejected while the alternative hypothesis is accepted, and hence there is existence of long run equilibrium relationship among the captured variables in the estimated equation. This outcome means that the explanatory variables have some long run relationship with the dependent variable.

Table 3

ARDL Co-integration (Bounds) Test
Test Statistic	Value	K
F-statistic	8.951766	6
Critical Value Bounds	I0 Bound	I1 Bound
Significance Level:
10%	1.99	2.94
5%	2.27	3.28
1%	2.88	3.99
Decision:	Cointegration
LOWER BOUND @ 5% = 2.22
UPPER BOUND @ 5% = 3.49
Source: Authors’ computation using Eviews 10 (2024)

4.4 Granger causality

According to the Granger causality test result presented in Table 7 below, we reject the null hypothesis that real gross domestic product (RGDP) does not Granger cause human development index (HDI). We also reject the null hypothesis that per capita income (PCI) does not Granger cause human development index (HDI). Similarly, the null hypothesis that income distribution (IND) does not Granger cause human development index (HDI) was also rejected. The hypotheses based on the P-values are rejected at 5 per cent level of significances. Thus, indicating that there is a uni-directional causality moving from real gross domestic product, per capita income and income distribution to human development index. This thus means that real gross domestic product, per capita income and income distribution Granger causes human development index.

Table 4

Granger causality
Pairwise Granger Causality Tests
Null Hypothesis:	Obs	F-Statistic	Prob.	Decision
INF does not Granger Cause HDI	41	0.72073	0.4939	Accept
HDI does not Granger Cause INF		1.09042	0.3479	Accept
RGDP does not Granger Cause HDI	41	4.77940	0.0150	Reject
HDI does not Granger Cause RGDP		0.32691	0.7235	Accept
PCI does not Granger Cause HDI	41	4.69244	0.0426	Reject
HDI does not Granger Cause PCI		1.06697	0.3556	Accept
POV does not Granger Cause HDI	41	0.68427	0.5115	Accept
HDI does not Granger Cause POV		0.45020	0.6414	Accept
UNEM does not Granger Cause HDI	41	1.27715	0.2923	Accept
HDI does not Granger Cause UNEM		1.69789	0.1987	Accept
IND does not Granger Cause HDI	41	5.66309	0.0247	Reject
HDI does not Granger Cause IND		0.40856	0.6679	Accept
Source: Authors’ computation using Eviews 10 (2024)

4.5 ARDL long run estimated result analysis

Table 5a and 5b shows the result of the long run result with and without income distribution. The long run result with income distribution shows that a 10 per cent increase in inflation, poverty, unemployment and income distribution will lead to 5.22, 0.06, 0.18 and 0.14 per centage decrease in human development index (socio-economic development) respectively. While a 10 per cent increase in log of real gross domestic product and per capita income will cause human development index (socio-economic development) to increase by 17.05 and 4.72 per cent respectively. The result likewise shows that all the variables are statistically significant except inflation that is not statistically significant as its probability ratio is greater than the 5 per cent level of significance.

Similarly, the long run result without income distribution shows that that a 10 per cent increase in inflation, poverty and unemployment will lead to 0.007, 0.02 and 0.07 per centage decrease in human development index (socio-economic development) respectively. While a 10 per cent increase in log of real gross domestic product and per capita income will cause human development index (socio-economic development) to increase by 1.85 and 0.69 per cent respectively. The result equally shows that all the variables are statistically significant except inflation that is not statistically significant as its probability ratio is greater than the 5 per cent level of significance.

Table 5

**a: Long run (over parameterize) ARDL result with income distribution (IND)** Dependent variable: HDI
Variable	Coefficient	Std. Error	t-Statistic	Prob.
INF	-0.521670	0.004076	-1.294996	0.0735
LRGDP	1.704640	5.226085	2.326179	0.0504
LPCI	0.471556	1.383857	3.340755	0.0397
POV	-0.005963	0.019305	-5.308884	0.0432
UNEM	-0.018228	0.039954	-2.456238	0.0571
IND	-0.014742	0.047299	-3.311670	0.0411
C	13.16510	39.99866	3.329139	0.0482
Source: Authors’ computation using EViews 10 (2024)

Table 5

**b: Long run (over parameterize) ARDL result without income distribution (IND)** Dependent variable: HDI
Variable	Coefficient	Std. Error	t-Statistic	Prob.
INF	-0.000746	0.000620	-1.203141	0.2521
LRGDP	0.184701	0.102482	3.802270	0.0467
LPCI	0.069369	0.028033	2.474577	0.0292
POV	-0.000192	0.000489	-4.393017	0.0012
UNEM	-0.006708	0.002677	-2.505787	0.0276
C	1.500723	0.752630	1.993971	0.0694
Source: Authors’ computation using EViews 10(2024)

Interactive impact of income distribution

Comparatively, the empirical result as provided in Tables 5a and 5b proves and shows that income distribution has impact and it serves as a pass-through effect in causing HDI (socio-economic development) to increase or reduce further than when it is not included. This is seen in the coefficient value of INF, RGDP, PCI, POV and UNEM when income distribution is included been greater than the values when income distribution is not included. This thus seems that the diminish coefficient of INF, RGDP, PCI, POV and UNEM renders the inflation-income distribution nexus significant. This may suggest that successful implementation and management of income distribution may to a great extent, depending on the prevailing socio-economic development target cause a further reduction or increase in inflation.

4.6 ARDL short run Error Correction Model (ECM) estimated result analysis

Table 6 below shows the short run results of inflation, income distribution and socio-economic development equation. The error correction mechanism (ECM) has the correct sign and size. The ECM coefficient of -0.65 indicates that it takes about 65 per cent of the short run disequilibrium to adjust to the long run equilibrium within the year. The t-statistics of -10.83 showed that the error correction term is statistically significant at five per cent level of significance. R-squared value of 0.94 and the value of R-squared adjusted of 0.87 indicates that about 94 per cent of total variation in the HDI is explained by inflation (INF), log of real gross domestic product (LRGDP), log of per capita income (LPCI), poverty (POV), unemployment (UNEM) and income distribution (IND) and only six per cent was unexplained which may be accounted for by other factors not included in the model. The Durbin Watson (D-W) statistics of 2.17 indicates no autocorrelation in the model. Therefore, the results can be used for forecasting and economic simulation.

Table 6

Short run (Parsimonious) Error Correction Model result
Dependent Variable: D(HDI)
Variable	Coefficient	Std. Error	t-Statistic	Prob.
D(HDI(-1))	-1.044657	0.103699	-10.07394	0.0000
D(HDI(-2))	-0.549646	0.123597	-4.447090	0.0010
D(HDI(-3))	-0.176771	0.095877	-1.843724	0.0923
D(INF)	-0.000121	0.166419	-3.196987	0.0085
D(INF(-1))	-2.830005	0.121905	-0.738942	0.4754
D(INF(-2))	-2.166525	0.581549	-0.727416	0.4822
D(INF(-3))	-0.000125	0.698053	-4.472293	0.0009
D(LRGDP)	0.091831	0.017902	5.129777	0.0003
D(LRGDP(-1))	0.074777	0.022047	3.391742	0.0060
D(LRGDP(-2))	-0.066697	0.015928	-4.187295	0.0015
D(LPCI)	0.009152	0.008663	1.056381	0.3134
D(LPCI(-1))	-0.015534	0.007197	-2.158333	0.0539
D(LPCI(-2))	0.025597	0.005823	4.395565	0.0011
D(POV)	-0.000155	0.236855	-5.437210	0.0002
D(POV(-1))	0.000239	3.032541	7.881429	0.0000
D(UNEM)	-0.000449	0.000826	-0.543609	0.5976
D(UNEM(-1))	-0.000366	0.000786	-0.464841	0.6511
D(UNEM(-2))	-0.001731	0.000767	-2.257337	0.0453
D(IND)	0.000224	3.429555	6.541573	0.0000
D(IND(-1))	-9.542005	4.555001	-2.097166	0.0599
CointEq(-1)*	-0.651024	0.004713	-10.82528	0.0000
R-squared	0.940714
Adjusted R-squared	0.874841
Durbin-Watson stat	2.126576
Source: Authors’ computation (2024)

Transmission channel of income distribution

Having established the notion of inflation with the interactive link of income distribution, thus, for the reason that income distribution is a function of human development index, income distribution is also treated as an endogenous variable to ascertain the transmission channel as captured in Eq. 7 earlier stated as:

IND_t = λ₀ + λ₁INF_t + λ₂ln(RGDP) + λ₃PCI_t + λ₄POV_t + λ₅UNEM_t$\:\:+$ λ₄HDI_t + ε_t

The result as shown in Table 8 shows that inflation, log of real gross domestic product, per capita income and unemployment has a negative relationship with income distribution. While poverty and human development index has a positive relationship with income distribution. All the variables are not statistically significant except inflation and human development whose probability ratio are less than the 5 per cent level of significance.

Table 7

**Long run result income distribution as a dependent variable** Dependent Variable: D(IND)
Variable	Coefficient	Std. Error	t-Statistic	Prob.
INF	-3.057059	0.409661	-2.580328	0.0494
LRGDP	-24.73626	22.62268	-1.093428	0.3241
LPCI	-7.652588	9.859852	-0.776136	0.4728
POV	0.152633	0.100078	1.525142	0.1877
UNEM	-1.570992	1.072558	-1.464716	0.2029
HDI	626.9687	182.6250	3.433093	0.0186
C	140.9779	183.0859	0.770009	0.4761
Source: Authors’ computation (2024)

In determining the income distribution transmission channel through which inflation affects socio-economic development, the following multivariate chain function earlier stated was analysed. Income distribution channel transmission on inflation-socio economic development equation:

Where the product of the earlier identified significant values of

$\:\frac{\partial\:HDI}{\partial\:IND}$ = $\:\frac{\partial\:HDI}{\partial\:INF}$ * $\:\frac{\:\partial\:INF}{\partial\:IND}$ = $\:\beta\:$₁ * λ₁

$\:\frac{\partial\:HDI}{\partial\:INF}$ which is $\:\beta\:$₁ = -0.521670

$\:\frac{\:\partial\:INF}{\partial\:IND}$ which is λ₁ = -3.057059

and their product (i.e. $\:\beta\:$₁ * λ₁) yields − 1.594780 approximately.

This result shows that a 10 per cent increase in income distribution, will first go through inflation to produce an adverse effect on socio-economic development. The result thus suggest that an upward trend in income distribution, will have a negative pass-through effect on inflation before exacting a negative effect on socio-economic development. Thus the magnitude of effect of inflation on socio-economic development through income distribution is -1.59. This simply implies that a 10 per cent increase in income distribution will increase the impact of inflation causing socio-economic development to decrease by 15.9 per cent. The adverse effect of inflation on socio-economic development stems from the fact that within the study scope, empirical evidences have shown that the policies been implemented or set aside for this purpose (socio-economic development) are not been followed or properly implemented to the latter. For instance, from 1980 to 2023 despite government continuous effort at reducing poverty through various policies and scheme such as conditional cash transfer, government grants, zero per cent etc has continually hit the rock as there continues to exist poverty.

A similar issue is regards unemployment, enrolment in education etc for the sole purpose of increasing socio-economic development without recourse to income distribution. Also in terms of the fixing of interest rate, most Nigerians do not care about the deposit interest rate as all their income and motive for holding money is mostly for consumption. Moreso, commercial banks and lending houses do not oblige to implementing the deposit interest rate and are mostly interested in giving out short term loans which is mostly also use for consumption instead of savings or for investment. Most of these loans been collected however do not trickle down to creating employment which in turn would have increased the productive capacity, increase per capita income and reduce variation in income distribution so as to reduce inflation while increasing socio-economic development.

It should be noted that income distribution effect on inflation as shown in table 10 is statistically significant. This is seen in the low probability value 0.049 which is lower than the 5 per cent significant level. This simply means that an increase in inflation is directly responsive to affect socio-economic development through income distribution.

Moreso, the transmission effect of income distribution for the impact of inflation on socioeconomic develpment results is positive and statistically significant as can be seen in the probability level of 0.0186. This may also suggests that success in increasing socio-economic development in Nigeria may, to a great extent depend on the prevailing income distribution (Gini coefficient) which serves as a channel of transmission to be effective at curbing inflation.

4.7 Post estimation diagnostic tests of residuals

To ascertain the adequacy of the estimated equation, several diagnostic tests were conducted. The Ramsey RESET test was employed to check the condition of stability of the estimated model. Normality tests such as the Breusch-Godfrey serial correlation Lagrange Multiplier (LM) test and the autoregressive conditional heteroscedastcity (ARCH) test were employed to check the existence of the normality or adequacy of the estimated model. The results of the tests are summarized in Tables 8 and 9.

The Ramsey RESET test statistic of 2.38 with its high probability value of 0.06 showed that the estimated equation is stable. The Breusch-Godfrey serial correlation LM test statistic of 2.57 with its high probability value of 0.28 showed that there is no problem of autocorrelation in the model. This indicates that the residuals terms are independent and hence there is no autocorrelation in the estimated equation. Meanwhile, the Breusch-Pagan-Godfrey Heteroskedasticity test value of 8.65 with its high probability of 0.05 showed that there is no problem of heteroscedasticity and hence the disturbance terms are normally distributed. This is thus confirmed by the fact that the probability value of the observed Chi-squared is 0.399 is greater than the 5 per cent level of significance. Also the autoregressive conditional heteroskedasticity (ARCH) test value of 1.97 with its high probability of 0.17 also confirm there is no problem of heteroskedasticity.

TABLE 8: Breusch-Godfrey Serial Correlation LM, Breusch-Pagan-Godfrey Heteroskedasticity and Ramsey RESET Test

4.7.3. Stability Test Analysis

The Cumulative Sum (CUMSUM) and Cumulative Sum of Squares (CUMSUM SQ) tests were applied in order to examine the stability of the parameter after the ECM models were estimated. Figures 1 and 2 shows that both the CUMSUM and CUMSUM SQ statistics fall within the critical bounds of ± five per cent level of significance. This plots indicate that the coefficients of the results being estimated are stable in the long run and that there exists a long-run relationship between inflation and socio-economic development in Nigeria. This therefore implies that the coefficients are changing gradually.

4.8 Discussion of findings

From the analysis of the result of this study, it can be seen that inflation have negative and significant impact on socio-economic development in Nigeria with income distribution serving as a transmission mechanism. Some findings and implications can be highlighted from the result. First, the bounds test result shows the existence of a unique long-run relationship among the variables in the equation. Therefore, the null hypotheses of absence of co-integration is rejected while the alternative hypothesis is retained. This signifies the relevance of these variables and income distribution as a pass through mechanism in affecting socio-economic development .

This result shows that a unit increase in income distribution, will first go through the inflation, to produce an adverse minute effect on socio-economic development. Deduced point from the above, the estimate suggest that an upward trend in income distribution will have a positive pass-through effect on inflation, before exacting a negative effect on socio-economic development.

With regards the inflation and socio-economic development equation, the results reported in Table 5a shows that the sign of the interaction term is negative and highly significant at 5 per cent level of significant. Thus, we find the magnitude of INF, PCI, POV, UNEM decrease from − 0.52 to -0.0007, 0.47 to 0.07, -0.006 to -0.0003 and − 0.02 to -0.0007 respectively

The income distribution is negative implying that the more unequal is the income distribution, the higher the negative effect of inflation on socio-economic development in Nigeria. A wage increase with regards to income distribution, largely resulting from the deliberations of wages and salary commissions has been consistent in determining inflation. The main mechanism by which this is done is the announcement effect of the commission’s awards which usually reverberates to wage and non wage incomes so that every group/individual seeks to improve, or at least maintain its existing position relative to others. An extreme demonstration of this competition is borne out by the fact that in some cases producers and sellers increase the prices of their goods in anticipation of wage increases so as to bridge the gap in income distribution, usually to be followed by additional increases when the awards have actually been affected. Within the period under review, salaries were increased for an upward of about five times in Nigeria, each time characterized with increase in the prices of goods and services. These phenomena demonstrate the extent of the competitive behaviour of different economic and social groups in the economy for their share of the nations’ wealth. Examples include the Udoji award of 1973 and the Shehu Shagari’s salaries and wages review of 1980 respectively (Otto, 2011) and more recently the Buhari’s administration of wage increment in 2018.

Between 1941 and 2022 there has been about 17 of such wage reviews to close up income distribution. These wage increases, often are not matched with increase in productivity, as there is increase in the wage of the wealthy too and so lead to inflationary situations. Though exerting an inverse relationship with inflation, in all, income distribution is statistically significant in determining inflation. With an increase in the per centage of income distribution, inflation is expected to reduce. This is possible if the money in the hands of the few people is been channeled into productive use and invested rather than buying ostentatious goods. Thereby creating an increase in the supply of goods and services, increase GDP, reduce unemployment, per capita income will increase and hence reduce inflation. This is consistent with the studies of Muhibbullah and Mala Rani Das (2019), Heer and Sussmuth (2003)

The study examined the relationship between inflation, income distribution and socio-economic development in Nigeria using data spanning from 1981 to 2023, by employing the use of Augmented Dickey Fuller test, cointegration, Error Correction Model and other post test technique. The result of the studies shows that inflation and income distribution has a negative effect on socio-economic development. Similarly the result shows that inflation does not have any significant relationship with socio-economic development while income distribution is said to have a statistical significant with socio-economic development. Income distribution thus serves as a pass-through effect on inflation which is a path to socio-economic development in Nigeria.

From the observed findings of the study based on the relationship between inflation, income distribution and socio-economic development in Nigeria, the following recommendations are made: government should partner with the private sector to increase the work force of the country. By so doing the rate of unemployment would be reduced. It is thus believed that by increasing employment rate, real gross domestic product will increase, the population would be reduce, which would lead to an increase in per capita income and hence reduction in poverty. This then brings about an increase in socio-economic development of the country.

Author Contribution

1 wrote the main manuscript text. 1 and 2 prepared the methodology and the analysis. 1, and 3 interpreted the results and provided the data used. All the authors reviewed the manuscript.

Abang, S.O. (2023). Economic policies, income distribution and inflation in Nigeria. A Ph.D dissertation submitted to the Graduate School, University of Calabar, Calabar
Afolabi, Olayemi, (1995) Assessment of the impact of inflation on financial intermediation in the Nigerian banking sector. Nigeria Deposit Insurance Corporation Quarterly, Vol. 5 No 1
Albanesi, S. (2007). Inflation and inequality. Journal of Monetary Economics, Elsevier, 54 (4), pp. 1088–1114.
Ali, A.K. & Asfaw, D.M (2023). Nexus between inflation, income inequality, and economic growth in Ethiopia. PLoS One. 18(11): e0294454
Awe, A.A. & Rufus, O.O. (2012). Determinants of Income Distribution in the Nigeria Economy: 1977-2005 International Business and Management 5(1), 126-137
Bulir, A. (2010). Income inequality: Does inflation matter?, IMF Staff Papers 48 (1), pp. 139-159
Dale, H. J. (1954). The Functional Distribution of Income in the United States, Review of Economics and Statistics 1850-1952
David, O. K., Okoroafor, D.O.K, Adeniji, S.O & Olasehinde, T. (2018). Estimating and Forecasting the Impact of Inﬂation on Economic Growth in Nigeria Using Threshold Analysis. CBN Journal of Applied Statistics Vol. 9 No. 1
Ebi, B.O. & Aladejaje, S.A. (2022). Oil price transmission, deficit financing and capital formation. Jurnal Ekonomi Malaysia 5601-5609
Etuk, H. E. (2017). Statistical intervention analysis of Nigerian monthly inflation. CARD International Journal of Management Studies, Business and Entrepreneurship Research Vol. 2, No. 4
Eze, O. M and Nweke, A. M. (2017).Assessment of the effect of inflation on Niger’s Economic Growth: Vector correction model approach. European Journal of Businesss and Management. Vol. 9, No 15
Galli, R. & von der Hoeven, R. (2001). Is inflation bad for income inequality: the importance of the initial rate of inflation, International Labor Organization Employment Paper, 29.
Heer,B. Süssmuth, B. (2003). Inflation and wealth distribution. Cesifo Working Paper No. 835 Category 6: Monetary Policy and International Finance
Li, H. & Zou, H. (2002). Inflation, Growth, and Income Distribution: A Cross-Country Study, Annals of Economics and Finance, 3, pp. 85-101
Maku, A. O. & Adelowokan, O. A. (2013). Dynamics of inflation in Nigeria: An autoregressive approach. European Journal of Humanities and Social Sciences, Vol. 22, pp. 1-7.
Masha, I. (1995) Now perspective on inflation in Nigeria, CBN Economic and Financial Review, 38(2), 34 - 56
Monninn (2014). Inflation and income inequality in developed economies. CEP Working Paper 2014/1
Muhibbullah, M.D. & Das, M.R. (2019).The Impact of Inﬂation on the Income Inequality of Bangladesh: A Time Series Analysis. International Journal of Business and Technopreneurship Volume 9, No 2, pp 141-150
Nnanna, O. J., Alade, S.O., & Odoko, F.O. (2003). Contemporary Economic Policy Issues. Central Bank Nigeria Publications.
Okere, E. J. & Sanni T. A. (2005) Money and the Nigerian Financial System, Jeso International Publication: Owerri.
Okoh, A.S. & Ebi, B. O. (2013). Infrastructure, investment, institutional quality, and economic growth in Nigeria: An interactive approach. European Journal of Humanities and Social Sciences, Vol. 26, no. 1
Oxfam's global (2017) Even it up campaign. Oxfam International
Ozdemir Z.A., (2020). Dynamics of inflation, output growth and their uncertainty in the UK: an empirical analysis. The Manchester School, 78(6): p. 511–537.
Škare, M. & Stjepanovic, S. (2014). Income distribution determinants and inequality – international comparison, Amfiteatru Economic Journal, ISSN 2247-9104, The Bucharest University of Economic Studies, Bucharest, Vol. 16, Iss. 37, pp. 980-993
Tanwar, R. (2016). Nexus between inflation and economic development in India. International Journal of Humanities and Social Science Invention, 3(9): p. 63–67.
Udoh, N.S. & Aniete, I. (2018). A predictive model for inflation in Nigeria. CBN Journal of Applied Statistics Vol. 9 No. 2, 103-129
Uma, K .E, Eboh, F.E & Nwaka, I.D (2012). Stabilisation of the Nigerian Economy: An Assessment of the Effectiveness of the Monetary Policy, Brazillian Journal of Humanities and Social Management Science, 5(4), 33-50.
Wollie, G. (2018). The relationship between inflation and economic growth in Ethiopia. Budapest International Research and Critics Institute-Journal (BIRCI-Journal), 1(3): p. 264–271.

No competing interests reported.

Inflation, income distribution nexus. A pathway to Nigeria's long term socioeconomic development. A chain rule effect

Status:

Version 1

Abstract

Figures

1. INTRODUCTION

2. LITERATURE REVIEW AND THEORETICAL FRAMEWORK